SYLLABUS

Physics 8100

Electromagnetic Theory I

Prerequisite: Physics 6520 or equivalent

Poisson and Laplace equations, multipole expansions, potential problems in two and three dimensions, boundary value problems in free space and materials, magnetostatics. Development of field theory leading to Maxwell’s equations.

Textbook: J. D. Jackson, "Classical Electrodynamics." Third Edition.

Reference Books:

J. B. Marion, "Classical Electromagnetic Radiation."

P. Lorrain and D. Corson, "Electromagnetic Fields and Waves."

W. Hauser, "Introduction to the Principles of Electromagnetism."

Contents:

I. Introduction to Electrostatics

1. Coulomb’s law

2. Electric field

3. Gauss’s law

4. Differential form of Gauss’s law

5. Another equation of electrostatics and the scalar potential

6. Surface distributions of charges and dipoles and discontinuities in the electric field and potential

7. Poisson and Laplace equations

8. Green’s Theorem

9. Uniqueness of the solution with Dirichlet or Neumann boundary conditions

10. Formal solution of electrostatic boundary-value problem with Green Function

11. Electrostatic potential energy and energy density, capacitance

II. Boundary-Value Problems in Electrostatics: I

1. Method of images

2. Point charge in the presence of a grounded conducting sphere

3. Point charge in the presence of a charged, insulated, conducting sphere

4. Point charge near a conducting sphere at fixed potential

5. Conducting sphere in a uniform electric field by method of images

6. Green function for the plane, general solution for the potential

7. Green function for the sphere, general solution for the potential

8. Conducting sphere with hemispheres at difference potentials

9. Orthogonal functions and expansions

10. Separation of variables, Laplace equation in rectangular coordinates

11. A two-dimensional potential problem, summation of a Fourier series

III. Boundary-Value Problems in Electrostatics: II

1. Laplace equation in spherical coordinates

2. Legendre equation and Legendre polynomials

3. Boundary-value problems with azimuthal symmetry

4. Associated Legendre functions and the spherical harmonics Y_lm (q , f )

5. Addition theorem for spherical harmonics

6. Expansion of Green functions in spherical coordinates

7. Solution of potential problems with the spherical Green function expansion

IV. Multipoles, Electrostatics of Macroscopic Media, Dielectrics

1. Multipole expansion

2. Multipole expansion of the energy of a charge distribution in an external field

3. Elementary treatment of electrostatics with ponderable media

4. Boundary-value problems with dielectrics

5. Electrostatic energy in dielectric media

V. Magnetostatics

1. Introduction and definitions

2. Biot and Savart law

3. Differential equations of magnetostatics and Ampere’s law

4. Vector potential

5. Vector potential and magnetic induction for a long, straight current- carrying wire

6. Magnetic fields of a localized current distribution, magnetic moment

7. Force and torque on and energy of a localized current distribution in an external magnetic induction

8. Macroscopic equations, boundary conditions on B and H

9. Methods of solving boundary-value problems in magnetostics

10. Uniformly magnetized sphere

11. Faraday’s law of induction

12. Energy in the magnetic field